Mark the correct alternative in each of the following: The value of \( \lim _{n \rightarrow \inf...

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Mark the correct alternative in each of the following:
The value of \( \lim _{n \rightarrow \infty}\left\{\frac{1+2+3+\ldots+n}{n+2}-\frac{n}{2}\right\} \) is
(A) \( 1 / 2 \)
(B) 1
(C) \( -1 \)
(D) \( -1 / 2 \)
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